Home Improvement Questions? Ask a Handyman for Answers
My primary concern would be the expansive soil. Your contractor's approach is ok with a few modifications. First an explanation, expansive soil on a flat grade or one that slopes away from a wall would tend to expand vertically not exerting much force against the wall. Looks like your grade is pretty flat. But I don't like the jagged edge of soil on the back of the wall pour. I'd suggest at a minimum the soil be cut smooth so any vertical soil movement has nothing to "grab". A smooth plywood form on the back side would be better. Beyond that given the grade behind the wall and the fairly short height of the wall you should be OK.
You don't need a footing because the wall isn't support a load (like a house foundation). Like I said before when the grade is flat the expansive pressure tends to be vertical not horizontal (towards the wall). The re-bar in the wall is an appropriate measure to strengthen the wall. The only reason I can think of for not forming up the wall on both sides is for the contractor to save money.